Concentric buttons of different sizes for imaging and standoff correction

ABSTRACT

Disclosed is a method of estimating a property of an earth formation penetrated by a borehole. The method includes conveying a carrier through the borehole and performing a plurality of electrical measurements on the formation using a sensor disposed at the carrier and having a plurality of electrodes disposed in a concentric arrangement wherein a standoff distance between the sensor and a wall of the borehole has an influence on each electrical measurement in the plurality of electrical measurements. The method further includes determining an impedance for each electrical measurement in the plurality of electrical measurements and inputting the determined impedances into an artificial neural network implemented by a processor. The artificial neural network outputs the property wherein the outputted property compensates for the influence of sensor standoff distance on each electrical measurement in the plurality of electrical measurements.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation in part application of U.S. patent applicationSer. No. 13/046,096 filed Mar. 11, 2011 which is a continuationapplication of U.S. patent application Ser. No. 12/178,590 filed Jul.23, 2008, the entire disclosure of which is incorporated herein byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention disclosed herein relates to imaging of subsurfacematerials and, in particular, to embodiments of electrodes useful forresistivity imaging.

2. Description of the Related Art

Drilling apparatus used for geophysical exploration often includesensors for collecting information about ambient subsurface materials.Sensors may include ones such as those used for resistivity imaging.However, certain problems arise in the use of sensors in a drill string.For example, conventional corrections are performed with calipers andother devices measuring the distance (mechanical, acoustic etc.). Themain problem here is the different position of resistivity sensor andcaliper, which makes the correction procedure doubtful if vibrationoccurs.

Therefore, what is needed is a design which offers accurate measurementsof standoff at the same position as the resistivity measurements whenperforming measurement while drilling.

BRIEF SUMMARY OF THE INVENTION

Disclosed is a method of estimating a property of an earth formationpenetrated by a borehole. The method includes: disposing into theborehole a sensor having a plurality of return electrodes and at leastone transmitter electrode disposed in a concentric arrangement;injecting a first current of a first frequency into the formation byapplying an alternating current voltage between first selected ones ofthe plurality of return electrodes and the at least one transmitterelectrode; injecting a second current of a second frequency into theformation by applying an alternating current voltage between secondselected ones of the plurality of return electrodes and the at least onetransmitter electrode; measuring effective impedance for each of thecurrents; and estimating the property using the measurements of theeffective impedance for each of the currents; wherein the estimatingcompensates for an influence of standoff distances of the sensor on themeasurements.

Also disclosed is a system for estimating a property of an earthformation penetrated by a borehole, the system includes: a sensorconfigured to be disposed into the borehole, the sensor having aplurality of return electrodes and at least one transmitter electrodedisposed in a concentric arrangement; and a processor coupled to thesensor, the processor being configured to execute instructions thatimplement a method, the method includes: injecting a first current, I₁,of a first frequency, f₁, into the formation by applying an alternatingcurrent (AC) voltage between first selected ones of the plurality ofreturn electrodes and the at least one transmitter electrode; injectinga second current, I₂, of a second frequency, f₂, into the formation byapplying an alternating current (AC) voltage between second selectedones of the plurality of return electrodes and the at least onetransmitter electrode; measuring effective impedance, Z_(e), for each ofthe currents; estimating the property using the measurements of theeffective impedance, Z_(e), for each of the currents; wherein theestimating compensates for an influence of standoff distances of thesensor on the measurements.

Further disclosed is a non-transitory computer readable mediumcomprising computer executable instructions for estimating a property ofan earth formation penetrated by a borehole using a sensor disposed inthe borehole and comprising a plurality of return electrodes and atleast one transmitter electrode disposed in a concentric arrangement byimplementing a method that includes: injecting a first current, I₁, of afirst frequency, f₁, into the formation by applying an alternatingcurrent (AC) voltage between first selected ones of the plurality ofreturn electrodes and the at least one transmitter electrode; injectinga second current, I₂, of a second frequency, f₂, into the formation byapplying an alternating current (AC) voltage between second selectedones of the plurality of return electrodes and the at least onetransmitter electrode; measuring effective impedance, Z_(e), for each ofthe currents; estimating the property using the measurements of theeffective impedance, Z_(e), for each of the currents; wherein theestimating compensates for an influence of standoff distances of thesensor on the measurements.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter which is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The foregoing and other features and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings in which:

FIG. 1 depicts a sensor having a circumferential distribution of returnelectrodes along a drill;

FIG. 2 depicts effects of vibration and rotation of the drill onpositioning of the sensor shown in FIG. 1;

FIG. 3 depicts a sensor having an axial distribution of returnelectrodes along a drill;

FIG. 4 depicts aspects of an apparatus for conducting logging whiledrilling;

FIG. 5 depicts a sensor according to the teachings herein;

FIG. 6 is a graph depicting dependence of a geometric factor onstandoff;

FIG. 7 is a graph depicting dependence of a reactive part of theimpedance on standoff, where the curves are normalized to the largestreturn electrode;

FIG. 8 is a chart useful for estimating standoff as a function of realimpedance;

FIG. 9 is a circuit diagram effectively depicting aspects of standoffdependence for the sensor;

FIG. 10 is a flow chart providing an exemplary method for using thesensor of FIG. 5;

FIG. 11 depicts aspects of an exemplary embodiment of an artificialneural network;

FIG. 12 depicts aspects of a sensor having a center electrode and threering electrodes;

FIGS. 13 A-I, collectively referred to as FIG. 13, illustrate results oftesting to validate prediction capabilities of the artificial neuralnetwork;

FIGS. 14 A-E, collectively referred to as FIG. 14, illustrate results oftesting to validate prediction capabilities of the artificial neuralnetwork for the sensor for various standoff distances from the sensor toa wall of a borehole;

FIG. 15 illustrates one diagram that summarizes the testing results forthe various standoff distances; and

FIG. 16 presents one example of a method for estimating a property of aformation penetrated by a borehole.

DETAILED DESCRIPTION OF THE INVENTION

Disclosed are techniques for using a sensor having a plurality ofelectrodes arranged in a concentric manner. The techniques provide forcollection of data in challenging environments, such as downholeenvironments that include oil-based-mud. For a better appreciation ofthe teachings herein, and a context of the invention, consider thefollowing aspects provided with regard to FIGS. 1 and 2.

FIG. 1 illustrates an arrangement of a sensor with four buttonelectrodes (also referred to as “return electrodes 13”). The returnelectrodes 13 may be used for a variety of measurements, including thoseassessing a standoff distance, or simply “standoff 11.” Standoff 11 asdiscussed herein is a distance from an outer surface of a drill 10 (orother such equipment) to a wall of a borehole 2. As shown in FIG. 2,standoff 11 can vary as the borehole 2 typically does not includeregular surfaces.

The return electrodes 5 depicted are in four related yet slightlydifferent locations (shown as sensor electrodes “a,” “b,” “c,” and “d”).The use of such sensor electrodes provides for certain advantages whenperforming measurements and evaluating results. However, due todifferent positioning of each return electrode 13 on the drill 10, eachreturn electrode 13 measures a property of the borehole 2 at a differentposition. Therefore, assessment of standoff 11 with one return electrode13 will not be based on the same information as used by another returnelectrode 13.

Using such an arrangement of return electrodes 13, it is not possible touniformly apply the standoff correction. More specifically, measurementvalues have to be stored and an algorithm has to be applied. Usually,this takes place after one complete rotation. Further, and by way ofexample, due to vibration (frequency could be some Hz) the differentelectrodes have different distances by passing the same position. Inthis case, the correction applied for this position later would bewrong. This problem is more or less the same like for FIG. 3.

Another orientation, such as one shown in FIG. 3, where the buttons(i.e., return electrodes 13) may be positioned in vertical directionalong the drill string 10, is also problematic. In this embodiment,problems arise because the time delay depends on the rate of penetrationand is therefore larger. Variation in standoff 11 arises due tovibration of the drill 10 and irregular shape of the borehole 2, and isfurther complicated by a requirement to consider a rate of penetration.Because of vibration and longer time delay, it is not very likely thatone sensor electrode will monitor the same location as another sensorelectrode. Depending on distances between each of the sensor electrodes,the time delay may be long enough that the borehole shape may evenslightly change.

Referring now to FIG. 4, there are shown aspects of an exemplaryembodiment of an instrument 50 for conducting “logging-while-drilling”(LWD). The instrument 50 is included within a drill string 10 thatincludes a drill bit 4. The drill string 10 provides for drilling of aborehole 2 into earth formations 1. The drill bit 4 is attached to adrill collar 14. The drill string 10 may include a plurality ofcouplings 15 for coupling various components into the drill string 10.The drill string 10 is one example of a “carrier” for conveying theinstrument 50 through the borehole 2. In wireline logging, the carrieris an armored wireline configured to convey the instrument 50. Thewireline can also provide a communications medium for communicationsbetween the instrument 50 and remote components such as a processor orcomputer processing system.

Generally, the borehole 2 is filled with drilling mud. Drilling mud maybe introduced for a variety of reasons, including provision of apressure barrier. In some instances, it is advantageous to useoil-based-mud as the drilling mud. The instrument 50 disclosed herein isparticularly useful in the presence of oil-based-mud (OBM).

As a matter of convention herein and for purposes of illustration only,the instrument 50 is shown as traveling along a Z-axis, while a crosssection of the instrument 50 is realized along an X-axis and a Y-axis.

In some embodiments, a drive 5 is included and provides for rotating thedrill string 10 and may include apparatus for providing depth control.Control of the drive 5 and the instrument 50 is achieved by operation ofcontrols 6 and a processor 7 coupled to the drill string 10. Thecontrols 6 and the processor 7 may provide for further capabilities. Forexample, the controls 6 are used to power and operate sensors (such asantenna) of the instrument 50, while the processor 7 receives and atleast one of packages, transmits and analyzes data provided by the drillstring 10 and/or components therein. In various embodiments ofinstruments for logging while drilling (LWD), the instrument 50processes at least some of the data collected downhole.

Considering the instrument 50 now in greater detail, and also withreference to FIG. 5, in this embodiment, the instrument 50 includes aplurality of electrodes, and is referred to in the following discussionas a “sensor 50.” For convention, the electrodes of the sensor 50include at least one transmitter electrode 51 and a plurality of returnelectrodes 52. Each of the electrodes is separated from the otherelectrodes by an insulator 57. At least one sensor 50 may be disposed onan outer surface of the drill string 10 as deemed appropriate.

Generally, the sensor 50 includes a plurality of switches 53. Theswitches 53 provide for controlling application of voltage to each ofthe electrodes. In short, each of the switches 53 may be toggled toprovide for various arrangements of “firing” or energizing of eachelectrode. The voltage provided to each electrode may be of anyfrequency deemed appropriate, in any duration deemed appropriate, and inany combination as deemed appropriate. By controlling arrangement of theswitches 53, an apparent size of the return electrode 52 can bemodified. Thus, not only is the size of the return electrode modified,but if a ring is switched to opposite polarity, also the size of thetransmitter electrode is changed.

Generally, a power supply for the sensor 50 provides alternating current(AC) that is in a relatively high frequency, f, range (for example, ofabout 1 MHz to about 10 MHz). The sensor 50 may be operated atfrequencies, f, above or below this range. For example, the sensor 50may be operated in frequency ranges from about 100 kHz to 100 MHz.

In some embodiments, the return electrodes 52 are referred to as “sensorelectrodes” and in other embodiments may be referred to as “buttonelectrodes,” or simply as a “button.” In operation, the transmitterelectrode 51 provides for one pole of an electric dipole, while the atleast one return electrode 52 provides for the other pole. Accordingly,the sensor 50 makes use of a single electric dipole for electricimaging, generally at a high-frequency, f. Thus, it should be recognizedthat the terms “transmit” and “return” and the various forms of theseterms are merely illustrative of aspects of operation of the instrument50, particularly for embodiments using AC current, and are therefore notto be construed as limiting of the instrument 50.

In some embodiments, achieving different button sizes at one location isaccomplished by changing polarity of electrode rings for the returnelectrodes 52. That is, the switches may be arranged so that innerelectrode rings are dominating the outer rings or the other around. Morespecifically, only if the inner ring (c) has the same polarity as thebutton in the center (d), the polarity of the next outer ring (b) can beswitched to the polarity of the inner electrodes, etc. In this way, onecan guarantee that no alternating polarities are selectable. Of course,one should recognize that an apparent size of the transmitter electrodemay be altered. For example, the outer return electrode (a) may be setto a polarity of the transmitter electrode 51. Other combinations may behad.

Generally, the AC voltage source between the return electrode(s) 52 andtransmitter electrode 51 is applied to provide sufficient conditions forinjecting current, I, into the formation 1. During the operation, theelectrodes are generally maintained under an equivalent electricalpotential. An output of the sensor 50 includes impedance measuredbetween each return electrode 52 and the transmitter electrode 51.Generally, the sensor 50 is mounted on an outer surface of the drill 10and results in 360 degree coverage for imaging of the formation 1.

Although it is considered that the sensor 50 is generally operated withsupporting components as shown (i.e., the controls 6 and the processor7), one skilled in the art will recognize that this is merelyillustrative and not limiting. For example, in some embodiments, thesensor 50 may include at least one on-board processor 7.

Turning now to the invention in greater detail, in one embodiment (seeFIG. 5), a series of the measurement return electrodes 52 (denoted as“a,” “b,” “c,” and “d”) are placed on a single circumferential padattached to the drill 10. The return electrodes 52 of different sizesare separated by isolative gaps, each gap including an insulator 57. Thesource voltage of high frequency (generally of 1 MHz or above) isapplied between the transmitter electrode(s) 51 and the returnelectrode(s) 52. Generally, all of the return electrodes 52 are keptunder the same electrical potential driven by the applied voltage, V.Generally, the measured value is the complex impedance, Z, through eachreturn electrode 52, or combination of return electrodes 52. Thisarrangement provides capacitive coupling between the sensor 50 and theformation 1 and enables imaging of the formation 1 even in theconditions of a very resistive oil-based mud.

Using the sensor 50 as described above, users are effectively providedwith a sensor of varying sizes. This provides users with an ability to,among other things, estimate a dimension of the standoff 11 (thedimension being useful for correcting data collected from the formation1) and also to maintain a desired resolution during imaging (underconditions of variable standoff).

Equation (1) below provides a relationship where estimates of standoff11 may be determined. That is, by performing measurements with returnelectrodes 52 of different sizes and by applying Eq. (1), standoff 11may be estimated.G·Re(Ż)=R _(f)  (1);In Eq. (1), Re(Ż) represents a real part of measured impedance, R_(f),represents a resistivity of the formation, and G represents a geometricfactor.

It turns out that even in the presence of highly resistive drilling mud,the geometric factor, G, changes with the standoff 11. The changebecomes more pronounced for the more pronounced standoff and a smallereffective return electrode 52. This effect is illustrated in FIG. 6where mathematical modeling results of the geometric factor, G, arepresented. In this example, the results correspond to sizes of 16millimeters (mm), 24 mm, 32 mm and 48 mm. The operating frequency inthis example was 10 MHz, the distance from the center of the returnelectrode to the transmitter electrode was 96 mm. The resistivity,R_(f), (assuming a homogeneous formation) was 10 ohm-meters. As thisfigure shows, the geometric factor, G, of a large 48 mm return electrode52 does not depend on the standoff 11, if the standoff 11 is less thanabout 1.5875 centimeters (cm, or about 0.625 inches). For returnelectrodes 52 of 16 mm and 32 mm, the geometric factor, G, depends onthe standoff 11 in the whole analyzed range of standoffs. If correctionsare not made for this effect, the readings from small return electrodes52 will produce an inaccurate image. Accordingly, using an imaginarypart of the impedance for the corrections may address the inaccuracy.

As shown in FIG. 7, the normalized imaginary part of the impedancedepends differently on the standoff. That is, there is a smalldifference between impedances where standoff is about 0.3175 cm (0.125inches), while there is a significant difference between impedances atabout 1.27 cm (about 0.5 in). To quantify behavior of the imaginary partof the impedance for the different size electrodes, the curves of FIG. 7may be divided by the curve corresponding to 48 mm size returnelectrode. The result of the division is presented in FIG. 8 andrepresents a chart that is used for the standoff estimation. In order toperform the correction, a ratio between readings corresponding to anindividual return electrode and the 48 mm return electrode 52 should becalculated. Then, for a given size of the return electrode (as shown inFIG. 7) and calculated ratio (provided along the y-axis of FIG. 7) theresulting graph enables finding of a standoff value (shown along thex-axis). As soon as the standoff 11 is known, the correction chart, suchas the exemplary one provided in FIG. 6, may be used to find thegeometric factor, G, corresponding to the given size of return electrode52 and standoff 11.

In this process, a selection of readings that maintain acceptablevertical resolution under the conditions of variable standoff may bemade. In other words, under certain standoff conditions, readings fromthe small return electrodes 52 become non-recoverable. Even after beingcorrected for standoff, the readings cannot deliver an image of theformation 1. Under such circumstances, readings corresponding to thereturn electrode 52 which is less affected by the standoff may beselected over readings from the smaller return electrodes 52. Thesereadings are generally capable of providing an image of the formation 1.Modeling results demonstrate that an acceptable quality image isobtained when the size B return electrode 52 is at least three timesbigger than the standoff. Using this criterion, readings that providethe best image for the given (estimated) standoff may be adaptivelyselected. Under conditions of a rugose borehole, this selection issimilar to a low-pass filter, which filters out high frequency componentfrom the data. This effect is illustrated in FIG. 8.

In FIG. 8, results of mathematical modeling are presented for differentsizes of the return electrodes 52. These results are provided for ahomogeneous formation 1 and a rugose borehole. In this example, rugosityis simulated by changing the size of the borehole such that the standoffis periodically changing from 0.25 to 0.5 in. The width of the standoffvaries from about 0.5 inches to about 4 inches. As shown in FIG. 8, thesmaller the return electrodes, the bigger the effect of boreholeirregularities on the readings. The opposite is true as well. That is,effectiveness of suppression of false readings is increased with biggerreturn electrodes 52.

In the examples of FIGS. 6 and 7, the results were obtained under theassumption that resistivity of the oil-based mud, R_(obm), is about fiveor more orders of magnitude bigger than the resistivity of formation,R_(f). Although this assumption is generally valid for the vast majorityof practical cases, there are some borehole fluids that are lessresistive relatively to the formation. In this case, an additional stepthat includes correction for resistivity of the mud, R_(m), should beperformed. This correction may be based a technique such as the oneprovided below. Correction for the finite resistivity of the mud shouldbe performed at the first stage of the processing prior to the geometricfactor correction.

As an example of correction for less resistive mud, consider theeffective schematic circuit diagram presented in FIG. 9. The circuitprovided may be equated to aspects of the electric function of thesensor 50. This example shows that the measured effective impedance,Z_(e), depends on the internal impedance of the tool, Z_(T), theimpedance due to the gap between the sensor and the formation, Z_(G),and the formation resistivity, R_(f). For simplicity, it is assumed thatthere is no gap between the return electrode 52 and the formation 1. Forapplied voltage, U, and measured current, I, then the effectiveimpedance, Z_(e), is estimated by Eq. (2):

$\begin{matrix}{Z_{e} = {{Z_{T} + Z_{G} + R_{f}} = \frac{U}{I}}} & (2)\end{matrix}$

In case of a conductive formation (where resistivity of the formationR_(f)≦10 ohm-m) and oil-based mud, the contribution of the formationinto the effective impedance, Z_(e), is small (R_(f)<<<Z_(T)+Z_(G)) andit can be expected that a reduction of the sensitivity of the measuredimpedance to the resistivity of formation, R_(f). The gap impedance,Z_(G), which depends on the mud properties and the receiver standoff,becomes a major contributor into the effective impedance, Z_(e). Notethat in Eq. (2), Z_(T) represents an impedance of the sensor 50. Toextract the information about formation resistivity, R_(f),multi-frequency measurements may be employed prior to data processing.Consider using two frequencies. First, assume that impedancemeasurements have been conducted using a first frequency, f₁ and asecond frequency, f₂. Each frequency (f₁, f₂) permits estimation ofcorrelating effective impedances Z_(e1) and Z_(e2). This estimating maybe performed according to Eq. (3):

$\begin{matrix}{{Z_{e\; 1} = {{{{\mathbb{i}\omega}_{1}L} + R_{f} + \frac{1}{r^{- 1} + {{\mathbb{i}\omega}_{1}C}}} = {A_{1} + {{\mathbb{i}}\; B_{1}}}}},{Z_{e\; 2} = {{{\mathbb{i}\omega}_{2}L} + R_{f} + \frac{1}{r^{- 1} + {{\mathbb{i}\omega}_{2}C}} + A_{2} + {{\mathbb{i}}\; B_{2}}}}} & (3)\end{matrix}$where A₁, A₂ and B₁, B₂ correspond to the real and imaginary parts ofthe impedances Z_(e1) and Z_(e2), respectively. Eqs. (3) may berearranged as provided in Eqs. (4), and Eqs. (5):

$\begin{matrix}{{{A_{1} - A_{2}} = {r^{- 1}\left( {\frac{1}{r^{- 2} + \left( {\omega_{1}C} \right)^{2}} - \frac{1}{r^{- 2} + \left( {\omega_{2}C} \right)^{2}}} \right)}},{{\frac{B_{1}}{\omega_{1}} - \frac{B_{2}}{\omega_{2}}} = {- {C\left( {\frac{1}{r^{- 2} + \left( {\omega_{1}C} \right)^{2}} - \frac{1}{r^{- 2} + \left( {\omega_{2}C} \right)^{2}}} \right)}}}} & (4) \\{\frac{\frac{B_{1}}{\omega_{1}} - \frac{B_{2}}{\omega_{2}}}{A_{1} - A_{2}} = {G = {Cr}}} & (5)\end{matrix}$

Combining Eq. (5) with the first equation of Eqs. (4), resistivity ofthe gap, R_(g), may be found, as provided in Eq. (6):

$\begin{matrix}{R_{g} = {\left( {A_{1} - A_{2}} \right)/\left( {\frac{1}{1 + \left( {\omega_{1}G} \right)^{2}} - \frac{1}{1 + \left( {\omega_{2}G} \right)^{2}}} \right)}} & (6)\end{matrix}$

Equation (5) allows estimation of capacitance C between the returnelectrode 52 and the formation 1, while resistivity of formation, R_(f),may be derived from the Eq. (3), for example, by Eq. (7):

$\begin{matrix}{R_{f} = {{A_{1} - \frac{\left( {\omega_{1}C} \right)^{2}r}{r^{2} + \left( {\omega_{1}C} \right)^{2}}} = {A_{2} - \frac{\left( {\omega_{2}C} \right)^{2}r}{r^{2} + \left( {\omega_{2}C} \right)^{2}}}}} & (7)\end{matrix}$

Accordingly, and as depicted in FIG. 10, an exemplary and non-limitingmethod for estimating standoff 100 calls for selectively applyingvoltage to a plurality of concentric return electrodes and transmitterelectrode 101; measuring the impedance 102; and estimating standoffusing the measured impedance 103.

In summary, a method for imaging borehole wall resistivity with 360degree coverage in the presence of oil-based mud is described. A sensorfor the imaging includes a circumferential pad mounted on a drill andcontaining a series of variable size buttons electrodes (i.e., returnelectrodes) separated by insulating gaps. That is, a size of the buttonelectrode is determined by a number of ring electrodes having the samepolarity. The voltage source between symmetrical transmitting electrodesand sensor buttons is applied to provide sufficient conditions forinjecting current into the formation. An output of the sensor comprisesa measurement of the complex impedance for each sensor electrode. Theset of the buttons of different size provides enough flexibility toadjust imaging for the variable standoff conditions by correcting forthe variable standoff and selecting readings the best suitable for thedetermined standoff. The 360 degree coverage is achieved via combinationof the pad's shape, pad's azimuthal rotation, and a system to centralizethe position of the imager in the well.

Another approach to estimate resistivity or its inverse conductivity ofa formation while compensating for standoff effects is now discussed.The term “compensating” relates to estimating a value of a formationproperty that has increased accuracy due to reducing or eliminating anystandoff influences in measurements. In this approach, data from aplurality of formation measurements is input into an artificial neuralnetwork (ANN). The data includes real and imaginary parts of measuredformation impedance using various configurations of ring electrodes suchas the electrodes 52 a,b,c,d shown in FIG. 5. Examples of the differentelectrode configurations are presented below. Once the measurement datais input into the ANN, the ANN, which was previously trained, calculatesthe conductivity of the formation compensating for various standoffsthat occurred during the measurements.

Reference may now be has to FIG. 11, which depicts aspects of anexemplary embodiment of an ANN 110. The ANN 110 in FIG. 11 is amultilayer feed-forward (MLFF) network. The MLFF network shown has threelayers: an input layer, an output layer, and a hidden layer. The numberof neurons in the hidden layer is set to 16 in this embodiment. Anon-linear activation function in the ANN 110 in one embodiment isselected to a Tan-Sigmoid (Tansig) transfer function. For numericalreasons, the formation conductivity, σ_(F), is a logarithmical number.Hence, the ANN 110 can be configured to provide a logarithmical numberas output. It can be appreciated that the ANN 110 can be implemented bya processor such as in a computer processing system. The processor canbe disposed downhole at the carrier or at the surface of the earth. Theprocessor 7 (see FIG. 12) is one example of a processor for implementingthe ANN 110.

As noted above, various configurations of concentric electrodes are usedto perform formation conductivity measurements at various standoffs.FIG. 12 illustrates a side cross-sectional view of a sensor 120 having acenter electrode 124, a first ring electrode 121, a second ringelectrode 122, and a third ring electrode 123, which are similar to theelectrode configuration shown in FIG. 5. The ring electrodes 121-123 areconcentric with the center electrode 124. Not shown is a returnelectrode such as electrode 51 shown in FIG. 5 that may be used forreceiving current injected by the electrodes 121-124. Switches 125 andvoltage source 126 are configured to apply voltage V at frequency f tovarious combinations of the electrodes 121-124. The switches 125 arealso configured to connect selected ring electrodes to ground or to letselected ring electrodes float. Current (I) is injected through thestandoff and into the formation by the electrodes connected to thevoltage source 126. Injected current returns through the standoff to thereturn electrode or ring electrodes connected to ground. Currentresulting from applying the voltage V at selected electrodes is measuredto determine the real and imaginary parts of the measured impedance(Impedance=V/I). In the embodiment of FIG. 12, the controls 6 areconfigured to operate the switches 125. The processor 7 is configured toreceive voltage or current measurements performed by electrical sensors(not shown) at the electrodes 121-124 or the return electrode. Table 1presents one example of the various combinations and applications of theelectrodes 121-124 used for measuring the impedance of the formation.

TABLE 1 Electrode Center First Ring Second Ring Third Ring ConfigurationElectrode Electrode Electrode Electrode 1 Voltage V Ground Ground Groundapplied 2 Voltage V Voltage V Ground Ground applied applied 3 Voltage VVoltage V Voltage V Ground applied applied applied 4 Voltage V Voltage VVoltage V Voltage V applied applied applied applied 5 Voltage V FloatGround Ground applied 6 Voltage V Float Float Ground applied 7 Voltage VFloat Float Float applied 8 Voltage V Voltage V Float Float appliedapplied 9 Voltage V Voltage V Voltage V Float applied applied applied

For training purposes, twenty-eight data sets were input into the ANN110. For each data set, the standoff was 4 mm, the formationpermittivity was 10, the mud permittivity was 5 and the mud conductivitywas zero. Twenty-eight values of formation conductivity were inputranging from 0.001 S/m to 7000 S/m. Test frequency was in the 40-50 MHzrange.

Testing was performed to validate the prediction capabilities of the ANN110 for the nine electrode configurations listed in Table 1. FIG. 13illustrates the results of the test, which shows that matching betweenthe training data sets and the output (i.e., validation) data sets isvery good. The triangles represent calibration values while the dotsrepresent validation values. This test confirms that the ANN 110 is ableto predict the formation conductivity, σ_(F), in principle withoutambiguity.

Other tests were then performed to confirm that the ANN 110 cancompensate for standoff related influences or distortions. FIG. 14illustrates results of these tests for varying formation conductivitiesfor various constant values of standoff ranging from 1 mm to 12 mm at atest frequency of 50 MHz. The triangles represent calibration valueswhile the dots represent validation values. Associated with each graphin FIG. 14 are a coefficient of correlation R² and a performance ofcalibration expressed as the root mean square error of the calibration(or training) group (RMSE_(c)) and the validation group (RMSE_(v)). Theyshould be as low as possible and in the same order of magnitude. IfRMSE_(c) is considerably lower than RMSE_(v), the ANN 110 can beadjusted in order to remove this over fitting. As can be seen in thediagrams in FIG. 14, the ANN 110 is able to predict the conductivity ofthe formation with an accuracy of 0.148≦RMSE_(v)≦0.327. FIG. 15summarizes the results of these tests in one diagram. In FIG. 15, thetriangles represent calibration values while the dots representvalidation values.

FIG. 16 presents one example of a method 160 for estimating a propertyof an earth formation penetrated by a borehole. The method 160 calls for(step 161) conveying a carrier through the borehole. Further, the method160 calls for (step 162) performing a plurality of electricalmeasurements on the formation using a sensor having a plurality ofelectrodes disposed in a concentric arrangement wherein a standoffdistance between the sensor and a wall of the borehole has an influenceon each electrical measurement in the plurality of electricalmeasurements. Further, the method 160 calls for (step 163) determiningan impedance for each electrical measurement. Further, the method 160calls for (step 164) inputting each determined impedance into anartificial neural network implemented by a processor. Further, themethod 160 calls for (step 165) outputting the property from theartificial neural network wherein the outputted property compensates forthe influence of sensor standoff distance on each electrical measurementin the plurality of electrical measurements. Non-limiting examples ofthe property include resistivity, conductivity or an image of theborehole as a function of depth in the borehole using variations in theestimated property with depth. The method 160 can also include trainingthe artificial network by inputting a plurality of data sets where eachdata set includes sensor standoff, formation conductivity, formationpermittivity, borehole fluid conductivity, and borehole fluidpermittivity, and test frequency.

In support of the teachings herein, various analysis components may beused, including a digital and/or an analog system. For example, thecontrols 6 or the processor 7 may include the analog or digital system.The system may have components such as a processor, storage media,memory, input, output, communications link (wired, wireless, pulsed mud,optical or other), user interfaces, software programs, signal processors(digital or analog) and other such components (such as resistors,capacitors, inductors and others) to provide for operation and analysesof the apparatus and methods disclosed herein in any of several mannerswell-appreciated in the art. It is considered that these teachings maybe, but need not be, implemented in conjunction with a set of computerexecutable instructions stored on a non-transitory computer readablemedium, including memory (ROMs, RAMs), optical (CD-ROMs), or magnetic(disks, hard drives), or any other type that when executed causes acomputer to implement the method of the present invention. Theseinstructions may provide for equipment operation, control, datacollection and analysis and other functions deemed relevant by a systemdesigner, owner, user or other such personnel, in addition to thefunctions described in this disclosure.

Further, various other components may be included and called upon forproviding for aspects of the teachings herein. For example, a powersupply (e.g., at least one of a generator, a remote supply and abattery), motive force (such as a translational force, propulsionalforce or a rotational force), magnet, electromagnet, sensor, electrode,transmitter, receiver, transceiver, antenna, controller, optical unit,electrical unit or electromechanical unit may be included in support ofthe various aspects discussed herein or in support of other functionsbeyond this disclosure.

The term “carrier” as used herein means any device, device component,combination of devices, media and/or member that may be used to convey,house, support or otherwise facilitate the use of another device, devicecomponent, combination of devices, media and/or member. The logging tool10 is one non-limiting example of a carrier. Other exemplarynon-limiting carriers include drill strings of the coiled tube type, ofthe jointed pipe type and any combination or portion thereof. Othercarrier examples include casing pipes, wirelines, wireline sondes,slickline sondes, drop shots, bottom-hole-assemblies, drill stringinserts, modules, internal housings and substrate portions thereof.

Elements of the embodiments have been introduced with either thearticles “a” or “an.” The articles are intended to mean that there areone or more of the elements. The terms “including” and “having” areintended to be inclusive such that there may be additional elementsother than the elements listed. The conjunction “or” when used with alist of at least two terms is intended to mean any term or combinationof terms. The terms “first,” “second” and “third” are used todistinguish elements and are not used to denote a particular order. Theterm “couple” relates to one component being coupled either directly toanother component or indirectly to the another component via one or moreintermediate components.

One skilled in the art will recognize that the various components ortechnologies may provide certain necessary or beneficial functionalityor features. Accordingly, these functions and features as may be neededin support of the appended claims and variations thereof, are recognizedas being inherently included as a part of the teachings herein and apart of the invention disclosed.

While the invention has been described with reference to exemplaryembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the invention. Inaddition, many modifications will be appreciated by those skilled in theart to adapt a particular instrument, situation or material to theteachings of the invention without departing from the essential scopethereof. Therefore, it is intended that the invention not be limited tothe particular embodiment disclosed as the best mode contemplated forcarrying out this invention, but that the invention will include allembodiments falling within the scope of the appended claims.

What is claimed is:
 1. A method of estimating a property of an earthformation penetrated by a borehole, the method comprising: conveying acarrier through the borehole; performing a plurality of electricalmeasurements on the formation using a sensor disposed at the carrier andhaving a plurality of electrodes disposed in a concentric arrangementwherein a standoff distance between the sensor and a wall of theborehole has an influence on each electrical measurement in theplurality of electrical measurements; determining an impedance for eachelectrical measurement in the plurality of electrical measurements;inputting each determined impedance into an artificial neural networkimplemented by a processor; and outputting the property from theartificial neural network wherein the outputted property compensates forthe influence of sensor standoff distance on each electrical measurementin the plurality of electrical measurements.
 2. The method as in claim1, wherein the property is conductivity or resistivity.
 3. The method asin claim 1, wherein the sensor comprises a central electrode surroundedconcentrically by a ring electrode.
 4. The method as in claim 3, whereinthe ring electrode comprises a plurality of ring electrodes.
 5. Themethod as in claim 4, wherein performing a plurality of electricalmeasurements comprises applying a voltage Vat frequency f to the centralelectrode.
 6. The method as in claim 5, wherein performing a pluralityof electrical measurements further comprises applying the voltage V atfrequency f to one or more of the ring electrodes.
 7. The method as inclaim 6, wherein performing a plurality of electrical measurementsfurther comprises switching one or more ring electrodes in the pluralityof ring electrodes that concentrically surround the central electrode toground or float using electrical switches that are configured to applyvoltage to various combinations of the ring electrodes.
 8. The method asin claim 6, wherein the frequency f comprises multiple frequencies. 9.The method as in claim 1, wherein each determined impedance comprises areal part and an imaginary part.
 10. The method as in claim 1, furthercomprising training the artificial neural network by inputting aplurality of data sets into the artificial neural network each data setin the plurality of data sets comprising electrical data associated witha standoff value.
 11. The method as in claim 1, further comprisingadjusting the artificial network to reduce a difference between rootmean square error of calibration data sets and root mean square error ofvalidation data sets.
 12. An apparatus for estimating a property of anearth formation penetrated by a borehole, the apparatus comprising: acarrier configured to be conveyed through the borehole; a sensordisposed at the carrier and comprising a plurality of electrodesdisposed in a concentric arrangement, the sensor being configured toperform a plurality of electrical measurements on the formation whereina standoff distance between the sensor and a wall of the borehole has aninfluence on each electrical measurement in the plurality of electricalmeasurements; a processor coupled to the sensor and configured toreceive the plurality of electrical measurements for determining animpedance for each electrical measurement, the processor comprising anartificial neural network configured to receive each determinedimpedance and to output the property wherein the outputted propertycompensates for the influence of sensor standoff distance on eachelectrical measurement in the plurality of electrical measurements. 13.The apparatus as in claim 12, wherein the sensor comprises a centralelectrode and surrounded concentrically by a ring electrode.
 14. Theapparatus as in claim 13, wherein the ring electrode comprises aplurality of ring electrodes.
 15. The apparatus as in claim 14, furthercomprising a power source configured to apply a voltage Vat a frequencyf to the central electrode.
 16. The apparatus as in claim 15, furthercomprising one or more switches configured to apply the voltage V at thefrequency f from the power source to various combinations of one or moreselected ring electrodes that concentrically surround the centralelectrode.
 17. The apparatus as in claim 16, wherein the one or moreswitches are further configured to switch the one or more selected ringelectrodes to ground or float.
 18. The apparatus as in claim 12, whereinthe property is conductivity or resistivity.
 19. The apparatus as inclaim 18, wherein the conductivity or resistivity is presented as animage of the borehole.
 20. The apparatus as in claim 12, wherein theartificial neural network comprises an input layer, a hidden layer, andan output layer, the hidden layer comprising at least sixteen neurons.21. The apparatus as in claim 12, where in the carrier comprises awireline, a slickline, a drill string or coiled tubing.
 22. Anon-transitory computer readable medium comprising computer executableinstructions for estimating a property of an earth formation penetratedby a borehole by implementing a method comprising: performing aplurality of electrical measurements on the formation using a sensordisposed at the carrier and having a plurality of electrodes disposed ina concentric arrangement wherein a standoff distance between the sensorand a wall of the borehole has an influence on each electricalmeasurement in the plurality of electrical measurements; determining animpedance for each electrical measurement in the plurality of electricalmeasurements; inputting each determined impedance into an artificialneural network implemented by a processor; and outputting the propertyfrom the artificial neural network wherein the outputted propertycompensates for the influence of sensor standoff distance on eachelectrical measurement in the plurality of electrical measurements. 23.The method as in claim 1, wherein the artificial neural networkcomprises a non-linear activation function that is a Tan-Sigmoidtransfer function.